Theoretical Population Biology最新文献

This study describes a compact method for determining joint probabilities of identity-by-state (IBS) within and between loci in populations evolving under genetic drift, crossing-over, mutation, and regular inbreeding (partial self-fertilization). Analogues of classical indices of associations among loci arise as functions of these joint identities. This coalescence-based analysis indicates that multi-locus associations reflect simultaneous coalescence events across loci. Measures of association depend on genetic diversity rather than allelic frequencies, as do linkage disequilibrium and its relatives. Scaled indices designed to show monotonic dependence on rates of crossing-over, inbreeding, and mutation may prove useful for interpreting patterns of genome-scale variation.

Settlement is a critical transition in the life history of reef fish, and the timing of this event can have a strong effect on fitness. Key factors that influence settlement timing are predictable lunar cyclic variation in tidal currents, moonlight, and nocturnal predation risk as larvae transition from pelagic to benthic environments. However, populations typically display wide variation in the arrival of settlers over the lunar cycle. This variation is often hypothesized to result from unpredictable conditions in the pelagic environment and bet-hedging by spawning adults. Here, we consider the hypothesis that the timing of spawning and settlement is a strategic response to post-settlement competition. We use a game theoretic model to predict spawning and settlement distributions when fish face a tradeoff between minimizing density-independent predation risk while crossing the reef crest vs. avoiding high competitor density on settlement habitat. In general, we expect competition to spread spawning over time such that settlement is distributed around the lunar phase with the lowest predation risk, similar to an ideal free distribution in which competition spreads competitors across space. We examine the effects of overcompensating density dependence, age-dependent competition, and competition among daily settler cohorts. Our model predicts that even in the absence of stochastic variation in the larval environment, competition can result in qualitative divergence between spawning and settlement distributions. Furthermore, we show that if competitive strength increases with settler age, competition results in covariation between settler age and settlement date, with older larvae settling when predation risk is minimal. We predict that competition between daily cohorts delays peak settlement, with priority effects potentially selecting for a multimodal settlement distribution.

Leveraging the simplicity of nucleotide mismatch distributions, we provide an intuitive window into the evolution of the human influenza A ‘nonstructural’ (NS) gene segment. In an analysis suggested by the eminent Danish biologist Freddy B. Christiansen, we illustrate the existence of a continuous genetic “backbone” of influenza A NS sequences, steadily increasing in nucleotide distance to the 1918 root over more than a century. The 2009 influenza A/H1N1 pandemic represents a clear departure from this enduring genetic backbone. Utilizing nucleotide distance maps and phylogenetic analyses, we illustrate remaining uncertainties regarding the origin of the 2009 pandemic, highlighting the complexity of influenza evolution. The NS segment is interesting precisely because it experiences less pervasive positive selection, and departs less strongly from neutral evolution than e.g. the HA antigen. Consequently, sudden deviations from neutral diversification can indicate changes in other genes via the hitchhiking effect. Our approach employs two measures based on nucleotide mismatch counts to analyze the evolutionary dynamics of the NS gene segment. The rooted Hamming map of distances between a reference sequence and all other sequences over time, and the unrooted temporal Hamming distribution which captures the distribution of genotypic distances between simultaneously circulating viruses, thereby revealing patterns of nucleotide diversity and epi-evolutionary dynamics.

We introduce a multi-allele Wright–Fisher model with mutation and selection such that allele frequencies at a single locus are traced by the path of a hybrid jump–diffusion process. The state space of the process is given by the vertices and edges of a topological graph, i.e. edges are unit intervals. Vertices represent monomorphic population states and positions on the edges mark the biallelic proportions of ancestral and derived alleles during polymorphic segments. In this setting, mutations can only occur at monomorphic loci. We derive the stationary distribution in mutation–selection–drift equilibrium and obtain the expected allele frequency spectrum under large population size scaling. For the extended model with multiple independent loci we derive rigorous upper bounds for a wide class of associated measures of genetic variation. Within this framework we present mathematically precise arguments to conclude that the presence of directional selection reduces the magnitude of genetic variation, as constrained by the bounds for neutral evolution.

Multi-type birth–death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth–death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes – such as environmental carrying capacity or frequency-dependent selection – entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth–death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble’s stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth–death model.

In this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on ${[0,1]}^n$, $n\in N$, with a Poisson$\left(N\right)$-distributed number of vertices and in which vertices are connected over an edge when they have a distance of at most $r_N$ with $r_N$ of order $N^{(\beta -1)/n}$ for some $0<\beta <1$. At a host infection many parasites are generated and parasites move along edges to neighbouring hosts. We assume that parasites have to cooperate to infect hosts, in the sense that at least two parasites need to attack a host simultaneously. We find lower and upper bounds on the invasion probability of the parasites in terms of survival probabilities of branching processes with cooperation. Furthermore, we characterize the asymptotic invasion time.

An important ingredient of the proofs is a comparison with infection dynamics of cooperative parasites in host populations structured according to a complete graph, i.e. in well-mixed host populations. For these infection processes we can show that invasion probabilities are asymptotically equal to survival probabilities of branching processes with cooperation. Furthermore, we build on proof techniques developed in Brouard and Pokalyuk (2022), where an analogous invasion process has been studied for host populations structured according to a configuration model.

We substantiate our results with simulations.

Understanding the conditions that promote the evolution of migration is important in ecology and evolution. When environments are fixed and there is one most favorable site, migration to other sites lowers overall growth rate and is not favored. Here we ask, can environmental variability favor migration when there is one best site on average? Previous work suggests that the answer is yes, but a general and precise answer remained elusive. Here we establish new, rigorous inequalities to show (and use simulations to illustrate) how stochastic growth rate can increase with migration when fitness (dis)advantages fluctuate over time across sites. The effect of migration between sites on the overall stochastic growth rate depends on the difference in expected growth rates and the variance of the fluctuating difference in growth rates. When fluctuations (variance) are large, a population can benefit from bursts of higher growth in sites that are worse on average. Such bursts become more probable as the between-site variance increases. Our results apply to many ($\ge$ 2) sites, and reveal an interplay between the length of paths between sites, the average differences in site-specific growth rates, and the size of fluctuations. Our findings have implications for evolutionary biology as they provide conditions for departure from the reduction principle, and for ecological dynamics: even when there are superior sites in a sea of poor habitats, variability and habitat quality across space determine the importance of migration.